Question

How do you integrate `f(x)=(2+x+2x^2-3x^3)(3-x+2x^2+2x^3)` using the product rule?

Answer 1

Explanation:

If `2+x+2x^2 -3x^3` =g(x) and `3-x+2x^2+2x^3`= h(x), then `int g(x)*h(x) dx=g(x) int h(x)dx - int d/dx g(x) int h(x)dx`. Accordingly,

`int g(x)*g(x) dx= (2+x+2x^2-3x^3)(3x-x^2/2 +2 x^3 /3 +2x^4 /4) -int (1+4x-9x^2)(3x-x^2/2 +2 x^3 /3 +2x^4 /4)dx`

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